Such a variable displacement swash plate type compressor (hereinafter, simply referred to as “compressor”) is disclosed in Patent Document 1. As shown in FIGS. 10 and 11, a compressor 100 disclosed in Patent Document 1 includes a housing 101, which has a cylinder block 102, a front housing member 104, and a rear housing member 105. The front housing member 104 closes the front end of the cylinder block 102 via a valve plate 103a, and the rear housing member 105 closes the rear end of the cylinder block 102 via a valve plate 103b. 
A through hole 102h is located at the center of the cylinder block 102. The through hole 102h receives a rotary shaft 106, which extends through the front housing member 104. The cylinder block 102 has cylinder bores 107 arranged about the rotary shaft 106. Each cylinder bore 107 houses a double-headed piston 108. The cylinder block 102 further has a crank chamber 102a. The crank chamber 102a accommodates a tiltable swash plate 109, which rotates when receiving drive force from the rotary shaft 106. Each double-headed piston 108 is engaged with the swash plate 109 via shoes 110. The front housing member 104 and the rear housing member 105 have suction chambers 104a, 105a and discharge chambers 104b, 105b, which communicate with the cylinder bores 107.
An actuator 111 is arranged at the rear end of the through hole 102h of the cylinder block 102. The actuator 111 accommodates the rear end of the rotary shaft 106. The interior of the actuator 111 is slidable along the rear end of the rotary shaft 106. The periphery of the actuator 111 is slidable along the through hole 102h. A pressing spring 112 is located between the actuator 111 and the valve plate 103b. The pressing spring 112 urges the actuator 111 toward the front end of the rotary shaft 106. The urging force of the pressing spring 112 is determined by the balance with the pressure in the crank chamber 102a. 
A part of the through hole 102h that is rearward of the actuator 111 communicates with a pressure regulating chamber 117, which is provided in the rear housing member 105, via a through hole in the valve plate 103b. The pressure regulating chamber 117 is connected to the discharge chamber 105b via a pressure regulating circuit 118. A pressure control valve 119 is arranged in the pressure regulating circuit 118. The amount of movement of the actuator 111 is adjusted by the pressure in the pressure regulating chamber 117.
A first coupling body 114 is arranged in front of the actuator 111 with a thrust bearing 113 in between. The rotary shaft 106 extends through the first coupling body 114. The interior of the first coupling body 114 is slidable along the rotary shaft 106. The first coupling body 114 is designed to slide along the axis of the rotary shaft 106 when the actuator 111 slides. The first coupling body 114 has a first arm 114a, which extends outward from the periphery. The first arm 114a has a first pin guiding groove 114h, which is provided by cutting out a part diagonally with respect to the axis of the rotary shaft 106.
A second coupling body 115 is arranged in front of the swash plate 109. The second coupling body 115 is fixed to the rotary shaft 106 to rotate integrally with the rotary shaft 106. The second coupling body 115 has a second arm 115a, which extends outward from the periphery and is located at a substantially symmetrical position with respect to the first arm 114a. The second arm 115a has a second pin guiding groove 115h, which extends through the second arm 115a in a diagonal direction with respect to the axis of the rotary shaft 106.
Two first supporting lobes 109a, which extend toward the first arm 114a, are provided on a surface of the swash plate 109 that faces the first coupling body 114. The first arm 114a is located between the two first supporting lobes 109a. The first supporting lobes 109a and the first arm 114a are pivotally coupled to each other by a first coupling pin 114p, which extends through the first pin guiding groove 114h. 
Two second supporting lobes 109b, which extend toward the second arm 115a, are provided on a surface of the swash plate 109 that faces the second coupling body 115. The second arm 115a is located between the second supporting lobes 109b. The second supporting lobes 109b and the second arm 115a are pivotally coupled to each other by a second coupling pin 115p, which extends through the second pin guiding groove 115h. 
To decrease the displacement of the compressor 100, the pressure in the pressure regulating chamber 117 is lowered by closing the pressure control valve 119. This causes the pressure in the crank chamber 102a to be greater than the pressure in the pressure regulating chamber 117 and the urging force of the pressing spring 112. Accordingly, the actuator 111 is moved toward the valve plate 103b as shown in FIG. 10. At this time, the first coupling body 114 is pushed toward the actuator 111 by the pressure in the crank chamber 102a. The movement of the first coupling body 114 causes the first coupling pin 114p to be guided by the first pin guiding groove 114h, so that the first supporting lobes 109a rotate counterclockwise. As the first supporting lobes 109a rotate, the second supporting lobes 109b rotate counterclockwise, so that the second coupling pin 115p is guided by the second pin guiding groove 115h. This reduces the inclination angle of the swash plate 109 and thus reduces the stroke of the double-headed pistons 108. Accordingly, the displacement is decreased.
In contrast, to increase the displacement of the compressor 100, the pressure control valve 119 is opened to introduce high-pressure gas (control gas) from the discharge chamber 105b to the pressure regulating chamber 117 via the pressure regulating circuit 118, thereby increasing the pressure in the pressure regulating chamber 117. This causes the pressure in the pressure regulating chamber 117 and the urging force of the pressing spring 112 to be greater than the pressure in the crank chamber 102a. Accordingly, the actuator 111 is moved toward the swash plate 109 as shown in FIG. 11. At this time, the first coupling body 114 is pushed by the actuator 111 and moved toward the second coupling body 115. The movement of the first coupling body 114 causes the first coupling pin 114p to be guided by the first pin guiding groove 114h, so that the first supporting lobes 109a rotate clockwise. As the first supporting lobes 109a rotate, the second supporting lobes 109b rotate clockwise, so that the second coupling pin 115p is guided by the second pin guiding groove 115h. This increases the inclination angle of the swash plate 109 and thus increases the stroke of the double-headed pistons 108. Accordingly, the displacement is increased.